Evaluation of the Condition of Ngancar Dam in Wonogiri Regency is Reviewed from the Safety Aspect of the Dam

DOI : 10.17577/IJERTV10IS060119

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Evaluation of the Condition of Ngancar Dam in Wonogiri Regency is Reviewed from the Safety Aspect of the Dam

Hendra Wahyudi

Civil Infrastructure Engineering Department, Institut Teknologi Sepuluh Nopember, Sukolilo, Surabaya, Indonesia

Abstract:- Ngancar Dam is one of the dams that managed by Balai Besar Wilayah Sungai (BBWS) Bengawan Solo. Ngancar Dam is built on Jarak river, precisely located in Selopuro Village in Baturetno Sub-district and geographically located at 7O48'5" LS and 110O53' 53" BT. In addition, ngancar dam is also a historical building because it was built during the Japanese colonial era in 1944. In 1976 The Republic Indonesia goverment built gajah mungkur, Then it made Ngancar Dam located upstream.

After approximately seventy-five years of more operation and various maintenance during the operation and the enactment of various regulations set by the government especially regulations issued by the Ministry of Public Works and Housing of Republic Indonesia No. 27/PRT/M/2015 on dams that emphasize the safety aspects of the operation process then it is necessary to conduct a review of the condition of ngancar dam if reviewed from the safety aspect of the dam after carrying out its function during this time.

By using hydrological analysis to calculate flood discharge and hydraulic analysis to calculate water depth and analyze cremation and stability analysis by using geostudio software 2012 and supported by non-instructional testing with hammer test method to know the strength of concrete quality.

The results show the condition of Ngancar dam is reviewed from the safety aspect of the dam is still in a safe state because in the event of maximum flood discharge (Qpmf = 256,487 m3/sec) there is no overtoping, no deformation in static conditions or dynamic conditions and cracking on the dam at the time of flood or normal water is still smaller than 0.1% of the discharge of the base flow that enters ngancar dam

Keywords : Ngancar Dam, Safety Aspects, Government Regulation and Safety

  1. BACKGROUND

    Ngancar Dam is one of the dams managed by Balai Besar Wilayah Sungai (BBWS) Bengawan Solo. Ngancar Dam is built on Jarak river, precisely located in Selopuro Village in Baturetno Sub-district and geographically located at 7O48'5" LS and 110O53' 53" BT. In addition, ngancar dam is also a historical building because it was built during the Japanese colonial era in 1944. In 1976 The Republic Indonesia goverment built gajah mungkur dam then it made Ngancar Dam located upstream.

    Ngancar Dam has the function to irrigate rice fields in Temon Irrigation Area which has an area of 637 hectares with intake building in the form of a sewer-shaped tapping tower with a diameter of 1.5 meters and has a length of 65.7 meters and is arranged with a regulatory door that has a width of 1 meter and a height of 1 meter Ngancar Dam is a dam of gound and stone layer with Zonal clay core with dam peak length of 179 meters and dam height of 20.5 m at elevation of +250.54 meters and peak width of 5 m, with a guard height of 0.9 m and has upstream slopes with a ratio of 1:3 and downstream slopes with a ratio of 1:1,5. This dam has a concrete building with a wide threshold with a width of 34.10 meters at an elevation of +248.70 meters above sea level with the ability to drain water by 201.73 m3/sec and has a launcher channel of 84.75 meters and has a type of olak pond as a water energy silencer in the form of USBR type III made of concrete. The dam is in flood condition at an elevation of

    +249.49 mdpl capable of accommodating flood water of 3.05 million m3 while in normal conditions with elevation + 248.70 meters above seam able to hold water of 2.15 million m3 and at minimum conditions at elevation + 236.18 mdpl able to hold water by 0.89 million m3.

    After approximately seventy-five years of more operation and various maintenance during the operation and the enactment of various regulations set by the government especially regulations issued by the Ministry of Public Works and Housing of Republic Indonesia No. 27/PRT/M/2015 on dams that emphasize the safety aspects of the operation process then it is necessary to conduct a review of the condition of ngancar dam if reviewed from the safety aspect of the dam after carrying out its function during this time.

  2. PROBLEM FORMULATION

    Based on the background described above, the research on " Evaluation of the Condition of Ngancar Dam in Wonogiri Regency is reviewed from the safety aspect of the dam" can be formulated the following problems namely how the safety condition of Ngancar dam if reviewed from the safety aspect to carry out its operations.

  3. PROBLEM LIMITATIONS

Research conducted with "Evaluation of The Condition of Ngancar Dam in Wonogiri Regency is reviewed from the safety aspect of the dam" has the following limitations:

  • Aspects of dam safety include hydrological and hydraulic aspects, structural aspects and aspects of the dam while the understanding of each aspect is to include

    1. Aspects of hydrology and hydraulics namely dams are able / safe to drain flood water so that there is no overtoping.

    2. Aspects of the stability of the dam body include the ability of the dam structure to withstand static loads as well as dynamic loads.

    3. This aspect of the spill includes the ability of dams to withstand water from piping hazards.

  • While the safety aspect in carrying out operations related to water availability in this study was not carried out review.

  1. EXPECTED BENEFITS AND OBJECTIVES The benefits and objectives to be achieved from this research activity are :

    1. The benefits of this research, when viewed from the science side, are expected to add to the benefits of science, especially the issue of dam safety.

    2. The benefits of this research can be used as a guideline for policy makers in managing dams because dams in addition to carrying benefits also save potential disasters.

  2. THE FOUNDATION OF THEORY.

    The design flood hydrograph in this study used nakayasu synthetic unit hydrograph method. With the following equation form:

    .

    Where:

    Qp = peak flood discharge (m3/secec) Ro = rain unit (mm)

    = 3,6(0,3. + )

    0,3

    Tp = time log from the beginning of the rain to the peak of the flood (hours)

    T0.3 = time required by decreased discharge, from peak debit to 30% of peak debit (hours)

    Filtration capacity is water flowing into hili through the body and foundation of the dam based on the jarring of filtration flow routes that can be calculated by the following equations

    Figure 1. Trajektori network on a urugan dam

    = × × ×

    Where

    Qf = Rembesan capacity (m3/secec)

    Nf = the division number of the filtration flow route line Np = the number of divisions of the equipotensial line K = filtration coefficient (m3.dt)

    H = total water pressure height (m) L = Transverse profile length

    A dam is declared safe against cracking that occurs when the critical rembesan speed (Vc) > the speed of the spill (Vs). Rembesan analysis uses geostudio seep/w software based on finite element. The result of the calculation is flux i.e. discharge (Q) of the spillway that passes through the dam with the treatment of the surface condition of the reservoir in a flood state (FWL) and the condition of the reservoir in normal water conditions (NWL).

    The stability of he dam slope is analyzed using the Bishop method assuming the total normal force works in the center of the piece base and can be determined by deciphering the force on the piece vertically (normal). Balance requirements on the pieces that make up the slope as seen in the following image

    Figure 2 Style styles that work on a slice

    Description:

    W = Total weight on slices

    EL, ER = Style between slices working horizontally on the left and right cross section XL, XR= The style between slices that work vertically on the left and right cross section P = Total normal style on slices

    T = Slide style on the base of the slice B = Width of slice

    L = Length of slice

    = Slope Angle

    Taking into account the entire balance of styles then the formula for the security factor (Fk) of the Bishop method is obtained with the following equations

    =

    [ + ( ) tan ]

    sin

    With the level of security factor value presented in the table Table 1 Fk security value level in practice

    Fk

    Description

    >1,5

    Stable

    1,07<Fk<1,5

    critical

    <1,07

    Unstable

  3. Research Method.

    The research method is the whole stage of research conducted from start to finish so that a conclusion can be drawn. The steps can be seen in Figure 3. the following.

    Figure 3. Research Flow Chart

  4. RESULTS AND DISCUSSIONS.

    Hydrology Analysis is a basic analysis that must be done to evaluate the safety of the dam because the overall analysis of the water building of the pumping system depends on this analysis. Hydrology analysis in this study used data from TRMM from 2000 to 2019 as calibration data while stations around the site include Baturetno, Giriwoyo, Ngancar and Batuwarno stations because the data at the surrounding stations is incomplete especially from Batuwarno station no data from 2004 to 2011 with a watershed area of 693.7 hectares. For more details of thiesennya watershed and polygon shape can be seen in Figure 4

    Figure 4. Thiesen Watershed and Polygon Shapes

    By knowing the rain of the area with thiesen polygon, it is determined rain plan while to determine the size of the flood plan by using nakayasu method. The results of the flood discharge plan can be seen in Table 2

    Table 2 Debit Flood Plan

    No

    Reset

    Debit (m3/S)

    1

    5

    59.495

    2

    10

    71.157

    3

    25

    91.136

    4

    50

    107.739

    5

    100

    128.628

    6

    200

    154.590

    7

    1000

    229.892

    8

    ½ PMF

    132.743

    9

    PMF

    256.487

    Debit Maksimum (m3/dt)

    Debit Maksimum (m3/dt)

    The flood discharge plan is checked by Creager method with the results can be seen in Figure 5

    10000

    Grafik Creager

    10000

    Grafik Creager

    1000

    C30 C80 C100

    Q PMF Nakayasu Q PMF Gama-I Q PMF ITB-1

    Q PMF ITB-2

    1000

    C30 C80 C100

    Q PMF Nakayasu Q PMF Gama-I Q PMF ITB-1

    Q PMF ITB-2

    10

    10

    0

    1

    10

    A (km2)

    100

    1000

    0

    1

    10

    A (km2)

    100

    1000

    100

    100

    Figure 5. Creager Method Graph

    To evaluate the safety of dams against the danger of overtoping, a flood search is carried out on reservoirs that pass through the reservoir with the form of flood tracing as in figure 6

    Figure 6 Hydrograph of Ngancar Dam Flood Search While flood search results against high guard can be seen in the following table 3

    Table 3. Water level elevation at Spillway with High guard

    Kala Ulang

    Banjir

    Q inflow Maks

    Q outflow

    Maks

    Hd Maks

    Reduksi Puncak Banjir

    Elevasi Muka

    Air

    Tinggi Jagaan

    (parapet)

    Keterangan

    ( m3/det )

    ( m3/det )

    ( m )

    ( m3/det )

    ( % )

    ( m )

    ( m )

    Q 100 th

    Q 1000 th

    128.63

    229.89

    82.83

    163.10

    1.21

    1.85

    45.79

    66.79

    35.60%

    29.05%

    249.915

    250.550

    1.19

    0.55

    Tidak Overtopping Tidak Overtopping

    Q ½PMF

    132.74

    93.42

    1.31

    39.33

    29.63%

    250.010

    1.09

    Tidak Overtopping

    Q PMF

    265.49

    201.73

    2.11

    63.76

    24.02%

    250.808

    0.29

    Tidak Overtopping

    Kondisi Muka Air Normal 248.70 2.40

    Elevasi Puncak Bendungan 250.50

    Elevasi Parapet Puncak Bendungan 251.10

    From the hydraulic aspect done with a review of the ability of pelimpah to drain floods, the results can be seen in Table 4

    Table 4 Water face in pelimpah when flooding

    Kala Ulang

    Debit Banjir

    Elevasi Muka

    Air

    Tinggi Muka

    Air

    Kecepatan Air Pada

    Saluran Pengarah

    Keterangan

    (m³/dt)

    (mdpl)

    (m)

    (m/dt)

    (Kecepatan < 4 m/dt)

    Q 100th Q 1000th

    79.535

    158.472

    249.884

    250.518

    1.184

    1.818

    1.98

    2.57

    Aman Aman

    Q 1/2PMF

    89.942

    249.979

    1.279

    2.07

    Aman

    Q PMF

    195.163

    250.785

    2.085

    2.76

    Aman

    Elevasi Puncak Dinding

    251.180

    2.480

    Elevasi Crest Pelimpah

    248.700

    Analysis of dam body stability using geostudi software with a review of normal water conditions, flood water conditions and rapid low tide conditions can be seen in tables 5 through Table 11

    Table 5. Stability of Ngancar dam body against landslides under normal water conditions

    Table 6. Stability of Ngancar dam body against landslides in flood water conditions

    Table 7 Stability of Ngancar Dam Body against landslides in rapid low tide conditions

    Table 8. Deformation checks due to simulation of avalanche in empty conditions

    Beban

    Lereng

    ky

    Fk

    kmax (MDE)

    ky/kmax

    UM-8.5

    Keterangan UM-8.5

    Fk Simulasi

    y/h = 0.25

    Hulu

    0.564

    1.000

    0.727

    0.775

    0.10

    Tidak Terjadi Deformasi

    0.803

    y/h = 0.50

    Hulu

    0.579

    1.000

    0.785

    0.737

    0.65

    Tidak Terjadi Deformasi

    0.773

    y/h = 0.75

    Hulu

    0.579

    1.000

    0.732

    0.791

    0.45

    Tidak Terjadi Deformasi

    0.801

    y/h = 1.00

    Hulu

    0.550

    1.000

    0.678

    0.811

    0.20

    Tidak Terjadi Deformasi

    0.832

    Table 9. Deformation checks due to simulation of avalanche in normal water face conditions

    Beban

    Lereng

    ky

    Fk

    kmax (MDE)

    ky/kmax

    UM-8.5

    Keterangan

    Fk Simulasi

    y/h = 0.25

    Hulu

    0.666

    1.000

    0.727

    0.916

    0.90

    Tidak Terjadi Deformasi

    0.877

    y/h = 0.50

    Hulu

    0.695

    1.000

    0.785

    0.885

    0.60

    Tidak Terjadi Deformasi

    0.838

    y/h = 0.75

    Hulu

    0.669

    1.000

    0.732

    0.914

    0.40

    Tidak Terjadi Deformasi

    0.874

    y/h = 1.00

    Hulu

    0.640

    1.000

    0.678

    0.944

    0.19

    Tidak Terjadi Deformasi

    0.915

    Table 10. Deformation checks due to simulation of avalanche in flood water face conditions

    Beban

    Lereng

    ky

    Fk

    kmax (MDE)

    ky/kmax

    UM-8.5

    Keterangan

    Fk Simulasi

    y/h = 0.25

    Hulu

    0.648

    1.000

    0.727

    0.891

    1.83

    Tidak Terjadi Deformasi

    0.854

    y/h = 0.50

    Hulu

    0.669

    1.000

    0.785

    0.852

    0.89

    Tidak Terjadi Deformasi

    0.808

    y/h = 0.75

    Hulu

    0.669

    1.000

    0.732

    0.914

    0.80

    Tidak Terjadi Deformasi

    0.842

    y/h = 1.00

    Hulu

    0.620

    1.000

    0.678

    0.915

    0.80

    Tidak Terjadi Deformasi

    0.881

    Table 11. Deformation checks due to simulation of avalanche in rapid receding conditions

    Beban

    Lereng

    ky

    Fk

    kmax (MDE)

    ky/kmax

    UM-8.5

    UM-7.5

    Keterangan UM-8.5

    Fk Simulasi

    y/h = 0.25

    Hulu

    0.373

    1.000

    0.727

    0.513

    0.80

    0.12

    Tidak Terjadi Deformasi

    0.673

    y/h = 0.50

    Hulu

    0.368

    1.000

    0.785

    0.469

    100.20

    0.11

    Terjadi Deformasi

    0.650

    y/h = 0.75

    Hulu

    0.368

    1.000

    0.732

    0.503

    0.79

    0.11

    Tidak Terjadi Deformasi

    0.671

    y/h = 1.00

    Hulu

    0.373

    1.000

    0.678

    0.551

    0.67

    0.10

    Tidak Terjadi Deformasi

    0.694

    Test concrete strength by conducting non destructive test using hammer test tool at the location shown in figure 7.

    Figure 7 Location checking concrete strength with hammer test tool Non-instructive testing using the hammer method can be seen in Table 12

    Table 12. Hammer test results

    Code

    Location

    Test Result

    (Mpa)

    A

    Dinding Mercu Kiri

    38.28

    B

    Dinding Mercu Kanan

    40.33

    C

    Mercu Sisi Kanan

    41.56

    D

    Mercu Sisi Kiri

    35.44

    E

    Lantai Peluncur Atas

    35.61

    F

    Lantai Peluncur Bawah

    37.50

    G

    Blok Halang

    37.67

    H

    Dinding Peluncur Tengah Sisi Kiri

    34.67

    I

    Dinding Peluncur Tengah Sisi Kanan

    38.78

    J

    Lantai Peluncur Tengah

    41.78

    K

    Dinding Peluncur Bawah Sisi Kiri

    38.17

    L

    Dinding Peluncur Bawah Sisi Kanan

    36.00

    M

    Lantai Peluncur Bawah

    45.56

    N

    Blok Halang Bawah

    38.60

    Avarage

    38.57

    Based on non destructive test results with hammer test method shows concrete condition is still in good condition because the quality is greater than fc = 20.35 Mpa

    The simulation of rembesan on the body is reviewed in normal water face conditions, flooding and rapid receding which can be seen in figure 8 up to the following image

    Figure 8 Simulation of spills on the dam's body under normal water-front conditions

    A review of dam conditions resulting from the spillway during normal water review at point A shows the condition of the discharge of the water is 1,008 x 10-7 m3/secec < 1% Q baseflow = 0.0956 m3/secec while the safety factor against piping = 3,570 > 1.5 (safe)

    Figure 9 Simulation of the impact on the dam's body in flood water face conditions

    A review of dam conditions caused by the spill during normal water review at point A shows the condition of the discharge of the water is 1,089 x 10-7 m3/secec < 1% Q baseflow = 0.0956 m3/secec while the safety factor against piping = 3,256 > 1.5 (safe)

    Figure 10. Simulation of fracturing on the body of a dam at rapid receding conditions

    A review of dam conditions resulting from rapid low tide was reviewed at point A indicating a 4,729 x 10-8 m3/sec < 1% Q baseflow = 0.0956 m3/sec.

  5. CONCLUSION.

The conclusion of ngancar dam condition if reviewed from the aspect of dam safety are:

  1. Dam safety from hydrological and hydraulic aspects shows results in the event of PMF flooding of 265.49 m3/sec then pelimpah is able to drain flood discharge by 195,163 so that it does not overtoping occurred. Dam safety reviewed from the structural aspect shows a strong concrete flat press yield of 38.57 mpa > of the permitted minimum strength (fc = 20.35 Mpa) and at the time of static and dynamic conditions there is no deformation of the dam body.

  2. Dam safety is reviewed from the rembesan aspect showing the result of the spill result at the time of flood water level of 1,089 x 10-7 m3/sec < 0.0956 m3/sec.

concluded that the condition of ngancar dam is still in a safe state if it is reviewed from the safety aspect of the dam.

REFERENCE

  1. Anonim, 2015, Permen PUPR Nomor 27 tahun 2015 tentang Bendungan.

  2. Anonim, 1998, Dam Structures Surveys Paket SID C-5 : Laporan Rehabilitasi, tidak dipublikasikan

  3. Asdak, 2002. Hidrologi dan Pengelolaan Daerah Aliran Sugai. Gadjah Mada University Press. Yogyakarta.

  4. Bishop, A. W., 1955. The use of Slip Surface in The Stability of Analysis Slope, Geotechnique, Vol 5 London

  5. Bowles, J. E., 1984. Physical and Geotechnical Properties of SoilS, McGraw-Hill Book Company, USA

  6. DAS, Braja M,. 1985. Principle of Geothecnical Engineering, 3rd ed, Southern Illinois University, PWS Publishing Company, Boston

  7. Chow,1964, Handbook of Applied Hydrology, New York: Mc. Graw-Hill Book Company.

  8. Chow, V. T. , David, R. M., Larry, W. M. 1998. Applied Hydrology. New York

  9. Cordery, I. 1991. Estimation of Design Hydrograph for Small Rural Catchments. Journal of Hydrology No 13.

  10. Fan, J. and Morris, G. L. 1995. Reservoir Sedimentation Handbook: Design and Management of Dams, Reservoir and Watersheds for Sustainable Use. New York: McGraw-Hill.

  11. Frevert, R.K. 1959. Soil and Water Conservation Engineering. New York: John Wiley & Sons, Inc.

  12. Gordon, N. D., T. A. McMahon and B. L. Finalyson. 1992. Stream Hydrology An Introduction for Ecologist. John Wiley & Sons Ltd. New York.

  13. Gray, D. M. 1961. Synthetic Unit Hydrograhs for Small Watersheds. Journal of Hydroulic Div. ASCE. July. HY 4.

  14. Gray, D.M. 1970, Handbook on Principles of Hydrology. The Iowa State University Press, Ames, Iowa.

  15. Gregory, K. J. and D. E. Walling. 1977. Drainage Basin Storm and Process. Edward Arnold Publishing. Ltd. London.

  16. Gupta, S. N., A. P. Battacharya, S. R. Jindal. 1967. Statistical Correlation of Himalayan and Bundelkhand Basin Characteristics With Flood Flows, Floods and Their Computations, Proceeding of Leningrad Symposium, IASH, Unesco, WMO, Geneva.

  17. Haan, C.T., H.P. Johnson, and D. L. Brakenseik. 1982. Hydrologic Modelling of Small Watersheds. American Society of Agricutural Engineers

  18. Hadisusanto, N. 2011. Aplikasi Hidrologi. Malang: Jogja Mediautama.

  19. Hammer, W. I. 1978. Second Soil Conservation Consultant Report. Tech. Note No. 10. FAO/Centre for Soil Research Bogor. Indonesia.

  20. Hewlett, J. D. and W. L. Nutter, 1969. An Outline of Forest Hydrology. Athens: University of Georgia Press.

  21. Kennedy, J. and W. E. Watt. 1967. The Relationship Between Lag Time and the Phisical Characteristics of Drainage Basin In Southern Ontario. Flood and Their Computations. Proceeding of the Leningrad Symposium Vol III. IASH. Unesco. WMO. Geneva.

  22. Linsley, R.K., M.A. Kohler and J.L.H. Paulus. 1949. Surface Retention andDetention and overland Flow. Applied Hydrology. New York. Mc Graw Hill Book Co.

  23. Lewis K.V., 1975. Quantification of Soil Loss and Sediment Produced from Eroded Land. Soil Science. Soc. Am. J. Vol 24.

  24. Linsley, R.K., M.A. Kohler and J.L.H. Paulus. 1986. Hydrology for Engineers. Mc Graw Hill Book Co. New York.

  25. Mohraz, B,.1976. A Study of Earthquake Response Spectra For Different Geological Conditions, Bull. Of Seism. Soc. Of America, Vol 66, No 3., June. Pp 915-935.

  26. Mohraz., B., 1978., Influences Of The Magnetude of the Earthquake and the Duration of Strong Motion on Earthquake Response Spectra, Central American Conference on Earthquake Eng., San Salvador, CA, Jan 9-12, Proc., pp 27-35.

  27. Morgan, R. P. C. 1979. Topics in Applied Geography: Soil Erosion. Longman Group Ltd. London.

  28. Morgan, R. P. C. 1988. Soil Erosion. Longman Group Ltd. New York.

  29. Nash, J.E., and J.V. Sutcliffe, 1970. River Flow Forecasting Through Conceptual Models Part ICA Discussion of Principles, Journal of Hydrology. Vol 10.

  30. Saigal, S. and Mehrotra, D. (2012). "Performance Comparison of Time Series Data Using Predictive Data Mining Techniques", Advances in Information Mining, No. 1, Vol. 4

  31. SEED, H.B.; IDRISS, I.M., 1982, Ground Motions and Soil Liquefaction During Earthquakes , Earthq. Engineering Research Institute, Berkeley, California , Monograph, Libarary of Conggress Catalog Card Number 82-84224.

  32. SEED, H.B.; UGAS, C.; LYSMER, J., 1974, Site Dependent Spectra for Earthquake Resistant Design, University Of California, Berkeley, Earthquake Engineering Research Center, Report No. EERC 74-12, November, 14 pp.

  33. Sichuan Water Resources And Hydroelectric Investigation And Design Institute. 2010. Study Report On Dam Filling Material Of Jatigede Dam Project. Jakarta : Goverment of The Republic Of Indonesia Ministry Of Public Works Directorate General Of Water Resoure.

  34. Snyder, F. F. 1938. Synthetic Unit Graph. Trans Am Geophis Union. Report and Paper in Hydrology.

  35. Strahler, A. N. 1964. Quantitative Geomorphology of Drainage Basins and Channel Networks, in Handbook of Applied Hydrology, Ven Te Chow (ed). Mc Graw Hill. New York.

  36. Soemarto, CD. 1986. Hidrologi Teknik. Usaha Nasional. Surabaya.

  37. Soerjono, R. 1978. Kegiatan dan Masalah Kehutanan dalam DAS. Dalam Proceedings Pertemuan Diskusi. Pengelolaan Daerah Aliran Sungai. DITSI. Jakarta.

  38. Suripin, 2004. Pelestarian Sumber Daya Tanah dan Air. Penerbit Andi. Yogyakarta.

  39. Soewarno. 1995. Hidrologi Aplikasi Metode Statistik Untuk Analisa Data. Bandung Nova.

  40. Sosrodarsono dan Takeda, 1980. Hidrologi Untuk Pengairan. Jakarta: PT Pradnya Paramitra.

  41. Sri Harto, 1993. Analisa Hidrologi. Jakarta, PT Gramedia Pustaka Utama.

  42. Viessman, W., J. W. Knapp, G. L. Lewis, and T. E. Harbaugh. 1972. Introduction to Hydrology, Harper & Row Publishers, New York.

  43. Walpole, R.E., Myers, R.H., Myers, S.L., and Ye, K. 2007. Probability and Statistics for Engineers and Scientists. Eighth Edition. London: Pearson Education.

  44. Ward, R. S. 1974. Priciples of Hydrology. Second Edition. McGraw-Hill Book Company, Limited. London.

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